This publication surveys the differential geometry of types with degenerate Gauss maps, utilizing relocating frames and external differential varieties in addition to tensor equipment. The authors illustrate the constitution of types with degenerate Gauss maps, make sure the singular issues and singular kinds, locate focal photographs and build a type of the types with degenerate Gauss maps.

​​​​​​​​​​​​​​​​​​​​This quantity includes the invited contributions from talks introduced within the Fall 2011 sequence of the Seminar on Mathematical Sciences and purposes 2011 at Virginia kingdom college. individuals to this quantity, who're major researchers of their fields, current their paintings in how to generate actual interdisciplinary interplay.

It is a booklet on Euclidean geometry that covers the traditional fabric in a totally new method, whereas additionally introducing a couple of new subject matters that may be compatible as a junior-senior point undergraduate textbook. the writer doesn't commence within the conventional demeanour with summary geometric axioms. in its place, he assumes the genuine numbers, and starts his therapy through introducing such sleek strategies as a metric house, vector area notation, and teams, and therefore lays a rigorous foundation for geometry whereas even as giving the coed instruments that would be helpful in different classes.

A Fête of Topology: Papers devoted to Itiro Tamura specializes in the growth within the strategies, methodologies, and ways excited by topology, together with foliations, cohomology, and floor bundles. The booklet first takes a glance at leaf closures in Riemannian foliations and differentiable singular cohomology for foliations.